Inverse Fuction (1 Viewer)

lyounamu · Jul 28, 2008

http://www.boardofstudies.nsw.edu.au/hsc_exams/exam-papers-2007/pdf_doc/maths-ex1-07.pdf

Page 9 Q 6b)

I have got no clue. Can anyone help me on this?

midifile · Jul 28, 2008

lyounamu said:
http://www.boardofstudies.nsw.edu.au/hsc_exams/exam-papers-2007/pdf_doc/maths-ex1-07.pdf

Page 9 Q 6b)

I have got no clue. Can anyone help me on this?

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ther; mso-font-pitch:variable; mso-font-signature:0 0 0 0 0 0;} @font-face {font-family:Calibri; panose-1:2 15 5 2 2 2 4 3 2 4; mso-font-charset:0; mso-generic-font-family:swiss; mso-font-pitch:variable; mso-font-signature:-1610611985 1073750139 0 0 159 0;} /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin-top:0cm; margin-right:0cm; margin-bottom:10.0pt; margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;} p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing {mso-style-priority:1; mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;} .MsoChpDefault {mso-style-type:export-only; mso-default-props:yes; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi; mso-fareast-language:EN-US;} .MsoPapDefault {mso-style-type:export-only; margin-bottom:10.0pt; line-height:115%;} @page Section1 {size:612.0pt 792.0pt; margin:72.0pt 72.0pt 72.0pt 72.0pt; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style> i) f’(x) = ex + e-x which is greater than 0 for all values of x. Therefore f(x) is always increasing
<o>
</o> ii) Let y = ex - e-x
Swap x and y values:
x =ey - e-y = ey - 1/ey<o></o>
eyx = e2y - 1
e2y - eyx – 1 = 0
Now this is a quadratic with ey
Therefore ey = (x +- sqrt(x2 +4))/2
But ey is always greater than 0
So ey = (x + sqrt(x2 +4))/2
Therefore y = loge(x + sqrt(x2 +4))/2
f-I(x) = loge(x + sqrt(x2 +4))/2
<o></o>
iii) Sub 5 into the equation in part ii)
f-I(x) = loge(5 + sqrt(25 +4))/2
= 1.65 (2dp)
Therefore x = 1.65 (2dp)

lyounamu · Jul 28, 2008

midifile said:
<LINK href="file:///C:%5CUsers%5CMelissa%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel=File-List><LINK href="file:///C:%5CUsers%5CMelissa%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel=themeData><LINK href="file:///C:%5CUsers%5CMelissa%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel=colorSchemeMapping><STYLE>  </STYLE> i) f’(x) = ex + e-x which is greater than 0 for all values of x. Therefore f(x) is always increasing
<O>
</O>ii) Let y = ex - e-x
Swap x and y values:
x =ey - e-y = ey - 1/ey<O></O>
eyx = e2y - 1
e2y - eyx – 1 = 0
Now this is a quadratic with ey
Therefore ey = (x +- sqrt(x2 +4))/2
But ey is always greater than 0
So ey = (x + sqrt(x2 +4))/2
Therefore y = loge(x + sqrt(x2 +4))/2
f-I(x) = loge(x + sqrt(x2 +4))/2
<O></O>
iii) Sub 5 into the equation in part ii)
f-I(x) = loge(5 + sqrt(25 +4))/2
= 1.65 (2dp)
Therefore x = 1.65 (2dp)

That's awesome. I get it now. Thanks!

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Inverse Fuction (1 Viewer)

lyounamu

Reborn

midifile

Na Na Na Na Naa

lyounamu

Reborn

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